Thiago Catalan
Published 2016-01-15Version 1
We show that a $C^1-$generic non partially hyperbolic symplectic diffeomorphism $f$ has topological entropy equal to the supremum of the sum of the positive Lyapunov exponents of its hyperbolic periodic points. Moreover, we also prove that $f$ has topological entropy approximated by the topological entropy of $f$ restrict to basic hyperbolic sets. In particular, the topological entropy map is lower semicontinuous in a $C^1-$generic set of symplectic diffeomorphisms far from partial hyperbolicity.
An abstract continuity theorem for Lyapunov exponents of linear cocycles and an application to random cocycles
The dependence of Lyapunov exponents of polynomials on its coefficients
The approximation of Lyapunov exponents by horseshoes for $C^1$-diffeomorphisms with dominated splitting
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